Answer:
The possible values of x are 90°, 30° and 150°.
Step-by-step explanation:
Given that,
sin(2x) = cos(x) where 0° ≤ x < 180°
We know that, sin(2x) = 2 sinx cosx
2 sinx cosx = cosx
Subtract cosx on both sides
2 sinx cosx - cosx = 0
cosx (2sinx-1)=0
It means, cosx = 0 and (2sin x -1 ) = 0
cos x = cos0 and sinx = 1/2
x = 90° and x = 30°, 150°
Hence, the possible values of x are 90°, 30° and 150°.
